Properties

 Label 6720.l Number of curves $2$ Conductor $6720$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

Elliptic curves in class 6720.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.l1 6720bk2 [0, -1, 0, -5481, 158025] [2] 7680
6720.l2 6720bk1 [0, -1, 0, -336, 2646] [2] 3840 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 6720.l have rank $$0$$.

Complex multiplication

The elliptic curves in class 6720.l do not have complex multiplication.

Modular form6720.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + 6q^{11} - 4q^{13} + q^{15} + 6q^{17} + 6q^{19} + O(q^{20})$$

Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.